Can anyone out there help me ?
Q1. The lengths of the diagonals of a rhombus are 16 cm and 12 cm respectively.Find the length of each of its sides.
Q2. The sum of two opposite angles of a 11gm is 130 degrees. Find the measure of each of its angles.
Let ABCD is a rhombus and AC and BD are the diagonals that intersect each other at O. AC = 16 cm ; BD = 12 cm
Since diagonals of a rhombus bisect each other at right angle, then
∠ AOD = 900 and OA = OC = 8 cm ; OB = OD = 6 cm
Now, in Δ AOD ,
AD2 = AO2 + OD2
= (8)2 + (6)2
= 64 + 36
AD2 = 100
AD = 10 cm
So, each side of the rhombus is of 10 cm.
Let ABCD is a parallelogram.
∠ B + ∠ D = 1300
∠B + ∠B = 1300 ( Opposite angles of parallelogram are equal)
⇒∠B = 650 = ∠D
Now, ∠B + ∠C = 1800 (Adjacent angles of parallelogram are supplementary
⇒ ∠C = 1150
Now, ∠A = ∠C = 1150 (Opposite angles of parallelogram are equal)